Question

Two equal forces act on a particle then the angle between them when the square of their resultant is equal to three times their product is :

• A. ${90}^o$
• B. ${60}^o$
• C. ${45}^o$
• D. ${30}^o$

Answer 1

The correct option is B ${60}^o$

Let the magnitude of equal forces $=\lambda$
say $\theta$ be the angle between the forces
$\therefore$ the resultant of forces $=2\lambda \cos \frac{\theta }{2}$
According to the problem ${\left(2\lambda \cos \frac{\theta }{2}\right)}^2=3{\lambda }^2$
$\Rightarrow \frac{1+\cos \theta }{2}=\frac{3}{4}\Rightarrow \cos \theta =\frac{1}{2}\therefore \theta ={60}^o$